Michael A. Carpenter

Rejuvenation of metallic glasses by non-affine thermal strain

When a spatially uniform temperature change is imposed on a solid with more than one phase, or on a polycrystal of a single, non-cubic phase (showing anisotropic expansion–contraction), the resulting thermal strain is inhomogeneous (non-affine). Thermal cycling induces internal stresses, leading to structural and property changes that are usually deleterious. Glasses are the solids that form on cooling a liquid if crystallization is avoided—they might be considered the ultimate, uniform solids, without the microstructural features and defects associated with polycrystals. Here we explore the effects of cryogenic thermal cycling on glasses, specifically metallic glasses. We show that, contrary to the null effect expected from uniformity, thermal cycling induces rejuvenation, reaching less relaxed states of higher energy. We interpret these findings in the context that the dynamics in liquids become heterogeneous on cooling towards the glass transition, and that there may be consequent heterogeneities in the resulting glasses. For example, the vibrational dynamics of glassy silica at long wavelengths are those of an elastic continuum, but at wavelengths less than approximately three nanometres the vibrational dynamics are similar to those of a polycrystal with anisotropic grains. Thermal cycling of metallic glasses is easily applied, and gives improvements in compressive plasticity. The fact that such effects can be achieved is attributed to intrinsic non-uniformity of the glass structure, giving a non-uniform coefficient of thermal expansion. While metallic glasses may be particularly suitable for thermal cycling, the non-affine nature of strains in glasses in general deserves further study, whether they are induced by applied stresses or by temperature change.

Enthalpies of ordering in the plagioclase feldspar solid solution

Abstract Enthalpies of solution in lead borate at ~700°C have been measured for 36 natural and heat treated plagioclase feldspars. The samples made up two series, as characterised by TEM and XRD. A “low” series contained the natural ordered material and a “high” series the same samples annealed at high temperatures to induce cation disorder. Enthalpy of solution differences between the two series give the enthalpy changes associated with the disordering reactions: low albite → high albite: ~3 kcal/mole “e” structure → Cī high albite structure: ~ 1.4-2.8 kcal/mole Il structure →- Cl high albite structure: ~0.7-1.9 kcal/mole Il structure equilibrated at low temperature → Il structure equilibrated at high temperature: ~ 1.8−0.8 kcal/mole. ΔH soln data for the high series overlap with the data of Newton et al. (1980) for synthetic high structural state plagioclases except in the composition range ~An 90 –An 100 . They are consistent with an interpretation of the solid solution as being composed, at high temperatures, of two ideal (zero heat of mixing) segments, one with Cl symmetry and one with Il symmetry, and having a non-first order (continuous) order/disorder transformation between them. The low series can also be separated into two distinct trends, for Il and “e” structures. Values of the enthalpy change due to disordering ( ΔH ord ) also show a number of systematic trends. Firstly, the values for e → Cl are larger than for Il → Cl in the composition range where both e and Il structures are observed (~An 65 -An 72 ). Secondly, the enthalpy change on disordering the most ordered e structures at An-rich compositions is larger than for Ab-rich e structures. The apparent change in ΔH ord , which occurs at ~An 50 , may be important for the origin of the Boggild miscibility gap. Thirdly, the large enthalpy change of the e structure, due to ordering, may be sufficient to stabilise it relative even to a mixture of low albite plus anorthite. Values for the enthalpy change on disordering Il anorthites and bytownites to a Cl structure have been estimated by assuming that the Cl solid solution is ideal (non-enthalpic) and then extrapolating a straight line through the data for Ab-rich compositions to pure anorthite.

Mechanisms of exsolution in sodic pyroxenes

The free energy curves for simple binary solid solutions with limited miscibility or atomic ordering have been combined to predict the phase relations and exsolution mechanisms for a system in which both ordering and exsolution are possible. The nature of the ordering process affects which exsolution mechanisms may be used. If the ordering is second (or higher) order in character then continuous mechanisms predominate and a ‘conditional spinodal’ (Alien and Cahn, 1976) can be described which operates between ordered and disordered end members. For a first order case, the ordered phase can only precipitate a disordered phase by nucleation and growth.Microstructures in omphacites observed by transmission electron microscopy include exsolution lamellae and antiphase domains and the relations between them in selected specimens have been used to interpret the exsolution mechanisms which operated under geological conditions. It appears that most omphacites undergo cation ordering, and then remain homogeneous or exsolve a disordered pyroxene by spinodal decomposition. The predominance of continuous mechanisms has been used to indicate that the C2/c→P2/n transformation may be second (or higher) order in character.A possible phase diagram for jadeite-augite is presented. It is based on the idea that there should be limited miscibility between the disordered end members at low temperatures and that the cation ordering at intermediate compositions (omphacite) is superimposed on a solvus. It is adequate to explain many of the observed microstructures and fits with petrographic evidence of broad two phase fields between impure jadeite and omphacite and between omphacite and sodic augite. The effect of adding acmite is analogous to increasing temperature so that the phase relations for jadeite-acmite-augite can also be predicted.

High‐pressure elasticity of stishovite and the P42/mnm ⇌ Pnnm phase transition

A Landau free energy expansion has been developed to describe the elastic constant variations of stishovite (SiO2) associated with the P42/mnm (rutile-type) ⇌ Pnnm (CaCl2-type) phase transition as a function of pressure. The transition appears to display classical second-order character, with an equilibrium transition pressure which is renormalized by coupling of the soft optic mode with spontaneous strain. Lattice parameter data from the literature show that the symmetry breaking strain is large, while the nonsymmetry breaking strains are small. These have been used to constrain the numerical values of the strain/order parameter coupling coefficients, which in turn have been used to constrain values for the Landau coefficients. When substituted into expressions for all the individual elastic constants, taking values for experimental and calculated values of the bare elastic constants from the literature, a clear view of the pattern of elastic constant variations is produced. Variations of P and S wave velocities derived from the calculated elastic constants for a second-order transition show a dip as the transition point is approached from high pressure and from low pressure but do not show a discontinuity. The velocity anomaly provides a signature for the presence of free silica in the lower mantle.

Autocorrelation analysis of infrared spectra from minerals

The autocorrelation function, Corr(α, ω′) = \({\int}_{{-}{\infty}}^{{\infty}}\) α(ω + ω′)α(ω)dω, may be used to parameterise effective line widths of absorption bands in IR spectra. It has the advantage of not requiring any peak fitting to the primary spectra and can be applied to individual bands or groups of bands in a spectrum. A new procedure for analysing autocorrelation spectra which result from the application of the autocorrelation function to primary spectra is presented. The approach is well suited for quantifying line width variations in powder absorption spectra from sequences of samples with varying composition, degree of cation order or structural state. Worked examples are set out to illustrate different applications of the approach, including the characterisation of structural phase transitions in tridymite, Al/Si ordering under non-equilibrium conditions in Mg-cordierite, short range Al/Ge order in BaAl 2 Ge 2 O 8 feldspar and mixing behaviour in the jadeite-augite solid solution.

The synthesis, structure and electronic properties of a lead-free hybrid inorganic–organic double perovskite (MA)2KBiCl6 (MA = methylammonium)

In a search for lead-free materials that could be used as alternatives to the hybrid perovskites, (MA)PbX3, in photovoltaic applications, we have discovered a hybrid double perovskite, (MA)2KBiCl6, which shows strong similarities to the lead analogues. Spectroscopic measurements and nanoindentation studies are combined with density functional calculations to reveal the properties of this interesting system.

Phonon spectra of alkali feldspars; phase transitions and solid solutions

Abstract The phonon spectra of IR-active vibrations in alkali feldspars have been systematically investigated in the spectral range 50-2000 cm-1 at temperatures between 20 and 900 K. Samples with high degrees of Al-Si Order display IR absorption line profiles with spectral line widths that are systematically smaller than those for samples with low degrees of Al-Si order. Phonon frequencies depend in a nonlinear manner on the Na-K content, indicating nonideal mixing properties. The mode Grüneisen parameters are largest for low-frequency lattice modes and Si-O stretching modes; some negative Grüneisen parameters were found at phonon energies below 430 cm-1. The temperature evolution of the phonon spectra shows clear indications of the C2/m-C1̅ transition in Al-Si disordered Na-rich samples. An anomaly for highly Al-Si ordered microcline at 270 K is confirmed.

Novel phase transition in orthoenstatite

Abstract Single-crystal Brillouin scattering measurements on natural orthoenstatite [OEN] to 1350 °C at 1 atm show significant softening of the elastic moduli C33 and C55 ahead of a phase transition. To our knowledge, these are the first observations of acoustic mode-softening in orthoenstatite at high temperature and room pressure and could have important implications for Earths mantle. The phase transition is rapid and shows some hysteresis in the observed transition temperature, Ttr. Experiments performed on increasing and decreasing temperature bracket the transition temperature between 1090(10) °C ≤ Ttr ≤ 1175(10) °C, and pronounced acoustic mode-softening is evident at temperatures above 900 °C. Backscattering measurements to T = 1350 °C show no evidence for additional transitions. OEN was recovered at room temperature. Our results are interpreted in terms of elastic softening ahead of a displacive phase transition. Before the displacive transition can occur, however, the elastic softening appears to trigger the observed reconstructive transition to the more-stable protoenstatite (or high clinoenstatite) structure. We suggest that the displacive phase transition would lead to a previously unreported pyroxene structure with Cmca symmetry.

Strain analysis of phase transitions in (Ca,Sr)TiO3 perovskites

Abstract A single Landau free energy expansion is used to describe phase transitions in perovskites, from a cubic parent structure to tetragonal and orthorhombic structures with space groups related to the M3 and R25 points of the Pm3̅m reciprocal lattice. This expansion permits relationships between symmetry-adapted forms of the spontaneous strain and individual order parameter components to be predicted. Data from the literature for (Ca,Sr)TiO3 perovskites are analyzed in the light of these predictions. Shear strains for I4/mcm, Pnma, and Cmcm structures tend to conform to the predicted pattern. The Pm3̅m↔I4/mcm transition has nearly tricritical character as a function of temperature in CaTiO3 and more nearly second-order character as a function of composition at the Sr-rich end of the solid solution. Coupling with the volume strain appears to be both temperature and composition dependent, which may be a general feature of phase transitions in perovskites. Renormalization of fourth-order terms by changing the volume coupling coefficients could be responsible for the unusual order parameter evolution shown by CaTiO3 and for changes in thermodynamic character of the phase transitions as a function of composition. The pattern of strain variations also correlates closely with patterns of variations in heat capacity from the literature, suggesting revisions to the subsolidus phase diagram for the (Ca,Sr)TiO3 solid solution above room temperature.

Enthalpy effects associated with Al/Si ordering in anhydrous Mg-cordierite

Abstract Measurements of the heats of solution (ΔHsoln) in molten Pb2B2O5 at 708°C of anhydrous magnesian cordierites, prepared with a range of structural states, show that the enthalpy effect associated with Al/Si ordering is substantial (≳ 9.76 ± 1.56 kcal mole−1). Differences in the state of order between synthetic cordierites used in phase equilibrium studies and cordierites in the natural environment could lead to significant errors in the estimation of palaeo-pressures and temperatures. A continuous change of ΔHsoln with annealing time supports the suggestion of putnis (1980) that the hexagonal → orthorhombic transformation in cordierite, which can occur via a modulated structure, is truly continuous under metastable conditions. In addition, a linear relation between ΔHsoln and the logarithm of annealing time has been found, which provides some insight into the nature of the ordering mechanisms at an atomic level. Al and Si exchanges occur continuously between neighbouring tetrahedral sites with a net drift towards increasing order. No kinetic or thermochemical distinction can be made between the development of long range and short range order. The enthalpy of vitrification (~ 12 kcal mole−1) for a metastable stuffed β-quartz polymorph of cordierite composition is similar to that for pure quartz (on a per two oxygen basis), while the heat of vitrification for even the most disordered cordierite seen in this study is more than a factor of three greater (~40 kcal mole−1). This is consistent with the view that cordierite glass resembles the quartz structure more closely than the crystalline cordierite structure, and that crystallisation of the glass below ~900°C is controlled by a tetrahedral framework.